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POPULAR 



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LESSONS IN ASTRONOMY, 



ON A NEW PLAN; 



WHICH SOME OF THE LEADING PRINCIPLES OF THE SCIENCE ARE ILLUS- 
TRATED BY ACTUAL COMPARISONS, INDEPENDENT OF THE 
USE OF NUMBERS. 

) 



Ur*> 



FRANCIS J. GRUND 



AUTHOR OF "AN ELEMENTARY TREATISE ON PLANE AND SOLID GEOMETRY," "ELEMENTS OF NATURAL 
PHILOSOPHY AND CHEMISTRY." &C. 



BOSTON 



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CARTER, HENDEE AND CO 
1833. 



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Entered according to Act of Congress, in the year 1833, 

By Francis J. Grund, 
in the Clerk's office of the District Court of Massachusetts. 



/*'£/ 



I. R. BUTTS, SCHOOL STREET. 






NOTICE. 

The Geographical, which are used in the ^^f ^ „, 'eLily change 



them into 

the cubic miles by 64. 



PREFACE 



Although many elementary works on Astronomy are already before the public, yet it is 
believed there is none in which the various magnitudes, surfaces, and distances of the heavenly 
bodies, are presented to the eye of the learner by actual comparisons ; — the only way, perhaps, 
in which young pupils can be expected to form a correct idea of them. This the author has 
attempted in the following pages. The comparative diameters, surfaces. and distances of the 
different planets, are all drawn, in the plates, according to a fixed scale of geographical miles ; the 
surfaces of the planets are actually reduced to square measure, and drawn in proportion to each 
other and the sun ; so that the youngest pupil, by a mere glance of the eye, is enabled to form a 
correct idea of their respective magnitudes. A similar plan has been pursued, in regard to the 
division of the Earth into Zones, and with respect to the extent of the five great Continents of our 
Globe. The Appendix contains an exposition of the population of America, Europe, Asia, Africa, 
and Australia, accompanied by a plate for the illustration of the comparative settlements on those 
Continents. 

Boston, June 24, 1833. 



popular lessons in astronomy. 



LESSON I. 

THE EARTH IN ITS RELATION TO THE SUN, MOON AND STARS. 

^ 1. The Earth on which we live, and on which plants, trees and animals 
successively live and die, is only a small part of the w r orld ; it is but one of the 
smallest bodies in the Universe. To the world belong yet the Sun from which 
we receive warmth and light, the Moon, and an innumerable class of bodies, 
which, at night, appear to us as so many points of light. These are called Stars. 

The reason why the Stars appear to us so small, is because they are so far from us ; and things 
appear smaller in proportion as they are farther removed from us. This you will have noticed, 
when looking from a high steeple on the people below, or on a vessel far out in the harbour, or 
on a chain of mountains at a great distance. 

^ 2. Most all Stars appear to us, every night in the same position ; they seem 
actually to be fixed in the heavens ; and for this reason they are called fixed Stars. 
There are however Ten others, of which it has been ascertained that they move 
regularly round the Sun in large circles. These are called Planets or wandering 
Stars. — The fixed Stars are supposed to be similar to the Sun, in as much as they 
are bodies which have their own light. The Planets, on the contrary, are of 
themselves dark bodies, and receive, like our Earth, light and warmth from the 
Sun. We see them only in consequence of the solar light which they reflect 
from their surfaces, and this is the reason why they appear to us as bright as the 
other Stars. 

^ 3. The discoveries of Philosophers have proved beyond a doubt, that our 
Earth itself is one of those Planets, which move round the Sun in stupendous 
1 



2 POPULAR LESSONS [Less. I. 

large circles, whose grandeur is hardly conceived by the most powerful imagina- 
tion. Our Earth, therefore, is, itself, a Wandering Star, and the line in which 
it moves round the Sun is called its Way or Orbit. 

§ 4. The Planets, together with our Earth keep each a certain fixed distance 
from the Sun. On this account they do not disturb each other in their orbits. 
But they vary from each other in magnitude ; although all of them (consequently 
also our Earth) have a round shape, similar to a ball. 

In former times men believed that the Earth was flat, or a circular plate on all sides surrounded 
by water. But this is not true. For it has been proved by a great many observations and actual 
measurements, that the Earth has a spherical (ball-like) form. Moreover there are navigators 
who have actually sailed round the world, and who have noticed the fact that at sea, the tops of 
distant objects are seen sooner than the rest ; which again proves the spherical form of our 
Earth. For an illustration you may look at the adjoining plate Plate No. I. 

The man who is represented as standing on a portion of our Earth, will at first only see the 
topmast of a vessel at sea ; when she comes nearer his eye will discover a much greater portion 
of her ; but when in the third position every part of the vessel will be visible. 

§ 5. Some of the Planets are, in their motion round the Sun, accompanied by 
other dark bodies, which, like the Planets themselves, receive light and heat from 
the Sun. These are called Satellites or Moons. Such a Satellite is the Moon 
which accompanies our Earth ; and there are Planets (as we shall see hereafter) 
which have Four and Six, and One that has even Seven Moons. 

^ 6. Besides the Planets and Moons there is yet another class of bodies, 
moving round the Sun in exceedingly long ovals. They are but seldom visible, 
and are distinguished from other heavenly bodies by a tail which is often three, four, 
and more times larger than the body itself. These are called Comets ; but their 
number has not, as yet, been precisely ascertained. 

^ 7. The Planets, Moons and Comets, together with the Sun around which 
they move, form what is called our Solar System. But what will you say, if you 
are told that each fixed Star in the firmament is a Sun which, like our's, has its 
Planets and satellites and Comets ; in short, that each fixed Star is the centre of 
a solar system, a thousand and more times larger than our own ! ! But how in- 
finitely great must God's Creation appear to us, when we reflect that all these 
globes, as well as our own, may be inhabited by reasonable beings ! ! ! 



Less. L] IN ASTRONOMY. 



RECAPITULATION OF LESSON I. 

[If the pupil has learned and understood this lesson, it may perhaps be not unreasonable to sup- 
pose he will like to know something more about the Planets and the Moons in our system. But 
the teacher ought not to allow him to enter upon the second lesson, before he has recapitulated 
the first.] 

QUB-STIONS. 

[^ 1.] Does the Earth, or the globe on which we live, comprise the whole world 
which God has created ? Is our Earth any considerable portion of the Universe ? 
What other bodies belong to it ? Why do the Stars appear to us so small ? 

[^ 2.] Do all the Stars which we see remain in the same position ? What are 
those called which remain fixed? What, those, which are moving regularly- 
round the Sun ? What are the fixed Stars supposed to be ? Have the Planets any 
light of their own ? From what body do the Planets receive their light ? 

[^ 3.] What important discoveries have Philosophers made respecting the na- 
ture of our Earth ? 

What is the line in which our Earth moves round the Sun, called ? 

[^ 4.] Why do the orbits of the different Planets not disturb each other ? Are 
all Planets of the same magnitude ? What is their shape ? What is the shape of 
our Earth ? What reason have you to believe, that the Earth is round ? Explain 
Plate I ? 

[^ 5.] By what are some Planets in their motion round the Sun accompanied ? 
What are the bodies which accompany them called ? What body accompanies 
our Earth in its motion round the Sun ? Are there Planets which have more than 
One Moon? 

[^ 6.] What other class of bodies is there, besides the Planets and the Moons ? 
Are these bodies always visible ? By what are these bodies distinguished ? What 
are they called ? 

[^ 7.] What do the Planets, Moons and Comets, together with the Sun, round 
which they move, form ? What is each fixed Star supposed to be ? 



POPULAR LESSONS [Less. II. 



LESSON II. 

OF THE PLANETS AND THEIR RELATIVE POSITION WITH REGARD TO THE SUN AND EACH 

OTHER. 

^ 8. The Planets of which we have spoken in the First Lesson are Eleven in 
number, of which each has received a proper name. They are in the order in 
which they are placed from the Sun, the following : 

Mercury. Juno. 

Venus. Ceres. 

The Earth. Pallas. 

Mars. Jupiter. 

Vesta. Saturn. 

Herschel. 
The adjoining diagram, on Plate No. II, may serve for an illustration. You 
will see from it, that the Earth is the third Planet from the Sun. Mercury and 
Venus come before it ; the most remote from the Sun is Herschel, so called from 
the astronomer's name, who has but lately discovered it. 

^ 9. The Earth is constantly attended by One Satellite (Lesson I, ^ 5) ; Ju- 
piter by Four (see the diagram), Saturn by Six, and Herschel by Seven. Saturn 
is, besides, constantly surrounded by a broad luminous ring, which distinguishes 
it from all other Planets, and of which we shall speak hereafter. 

^10. With regard to the magnitude of the different Planets it has been ob- 
served that although some of them are much larger than Our Earth ; yet in Com- 
parison to the Sun they are but small bodies, as you may see from the figures on 
plate No. Ill, in which the different Planets are drawn in proportion to the Sun : 
you will perceive from it ; 

1 . That the Sun is a great many times * larger than either of the Planets. 

» Numbers are purposely omitted here, because abstract numbers convey little or no ideas to young 
pupils. Those who wish these relations expressed in numbers will find them in Table I at the end of 
the book. 







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Square contents <>/ ' -t/'X" s Surma* 
S quare contents of VESTd'S Surmce 

Square contents ofJktdRS'S Surrhce 
3 Square contents ofa\eE~ARTITS Surnu 

Square contents oftheMOOlfS Surrhce 
| Square contents of I'EXi'SS Surmci 

Square contents ofMURCURYS Surrace 



Less. II.] IN ASTRONOMY. 5 

2. That the Sun is much larger than all the Planets (our Earth included) 
taken together. 

3. That Jupiter is the greatest Planet in our solar system. 

4. That Saturn is the second Planet with regard to magnitude. 

5. That Herschel ranks third. 

6. That the Earth ranks fourth ; but that 

7. Each of the other Planets and the Moon are smaller than the Earth. 

8. That either of the Planets Ceres, Vesta, Juno, Pallas is smaller than the 
Moon. 

^11. If you cut a ball or a sphere in halves, and through the centre of one of 
the flat surfaces, draw a straight line across the whole surface, then this line is 
called the Diameter of the ball or sphere. — Now as the Sun and the Planets are 
nothing else but large balls or spheres (Lesson I, § 4), we may also speak of 
their Diameters. — Thus we say, " the Diameter of the Sun is so many times 
larger than that of the Earth ; the Diameter of Jupiter is so many times larger 
than that of Venus," etc. 

You will now easily understand what the straight line means, which, in plate No. Ill is 
drawn through the centre of the circle, which represents the Sun ; also the straight lines 
which are drawn through the circles which represent the Planets. — You will also perceive 
from the first figure on plate No. Ill, that the Sun's Diameter is larger than the Diameters of 
all the Planets taken together. 

^12. Plate No. IV represents the surfaces of the Planets, compared to that 
of the Sun. — For you must know that it is possible to measure the surface of 
a sphere ; which is done by supposing it to be spread out, and then seeing how 
many square inches, feet or yards it contains. This we have supposed to be done 
with the surfaces of the Sun and Planets, and accordingly, have drawn their 
square measurements, in Plate No. IV. in proportion to each other. 

You will see from this Plate : 

1. That the square-Contents of the Sun's surface is greater than that of the 
surfaces of all the Planets taken together. 

2. That the square-Contents of the Earth's surface is nearly as large as that 
of the surfaces of Mercury and Venus taken together. 

2 



6 POPULAR LESSONS [Less. II. 

3. That the square-Contents of the surfaces of Vesta, Ceres, Juno and Pallas, 
taken together, is not jet sufficient to cover the surface of our Earth. 

4. That the square-Contents of Jupiter's surface is larger than that of the sur- 
face of any other Planet. 

5. That the square-Contents of Jupiter's surface is greater than that of the 
surfaces of all other Planets taken together. 

6. That Saturn's surface is the next largest. 

7. That Herschel's is still larger than those of our Earth, Venus and Mercury 
taken together. 

8. That the square-Contents of the Moon is nearly as large as that of the sur- 
faces of Ceres, Vesta and Juno, taken together ; and that it is larger than that of 
Pallas' surface taken alone. 

In order that you may be better able to compare, you will find on Plate No. V 

1. The surfaces of the different Planets, all drawn upon the Sun's surface; 
from which you may see, how much larger the Sun's surface is than the surfaces 
of all the Planets and the Moon taken together. 

2. The surface of the Earth compared to that of Mercury and Venus. 

3. The Earth's surface compared to that of the Four Asteroids Pallas, Ceres, 
Juno and Vesta. 

4. Jupiter's surface compared to those of all the other Planets. 

5. The square-Contents of the Moon compared to the surfaces of Vesta, Juno 
and Ceres. 

6. Herschel's square-Contents compared to that of our Earth, Venus and Mer- 
cury taken together. 

^ 13. The Four Planets, Ceres, Vesta, Juno, and Pallas, are so small in propor- 
tion to the other Planets, and are so near each other (they are almost at the same 
distance from the Sun — see Plate II) that many distinguished philosophers are 
of opinion, they are but the fragments of One large Planet, which, from some 
cause or other, has burst. — But this is no subject for us now to inquire into ; — 
we will therefore proceed to describe in the next lesson, the motion of the dif- 
ferent Planets round the Sun. 



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Less. II.] IN ASTRONOMY. 



RECAPITULATION OF LESSON II. 

QUESTIONS. 

[§ 8.] What are the names of the Eleven Planets in the order in which they are 
placed from the Sun ? How many Planets are there between the Earth and the 
Sun ? How many Planets come after our Earth ? In what order then, is our 
Earth placed among the Planets ? (Is it the first, second, etc. from the Sun) ? 

[§ 9.] How many satellites accompany our Earth ? What is it called ? How 
many satellites or Moons has Jupiter ? How many has Saturn ? How many has 
Herschel ? By what is Saturn particularly distinguished from all other Planets ? 

[§ 10.] Are all Planets of the same magnitude as our Earth ? Are the Planets 
in comparison to the Sun large or small bodies ? — Is the Sun much larger than 
any of the Planets ? Is the Sun larger or smaller than all the Planets, including 
our Earth, taken together ? Which is the greatest of all Planets ? Which Planet 
ranks, in magnitude, next to Jupiter ? Which of the Planets ranks third in 
magnitude ? Which, Fourth ? What Planets are smaller than our Earth ? What 
Planets are smaller than the Moon ? 

[§11.] What do you call the Diameter of a ball or sphere ? Is the Diameter of 
the Sun larger or smaller than the Diameters of all the Planets taken together ? 

The teacher may yet ask a number of questions respecting the Diameters of the Planets, 
which the pupil will be able to answer by looking on Plate III. He may, for instance, ask 
whether the Diameter of the Earth is larger or smaller than that of Venus ? Whether the 
Diameter of Jupiter or Saturn is the largest, etc. ? This will oblige the pupil to compare the 
different magnitudes of the Planets and their Diameters. 

[§ 12.] What proportion does the square- Contents of the Sun's surface bear to 
that of the surfaces of all the Planets ? What two Planets have together a surface 
nearly as large as that of our Earth ? Are the surfaces of Ceres, Vesta, Juno and 
Pallas taken together sufficient or not, to cover the surface of our Earth ? What 
Planets, therefore, could be covered with the Earth's surface? Which Planet has 
the largest surface ? What do you observe with regard to the square-Contents of 



8 POPULAR LESSONS [Less. III. 

Jupiter's surface ? and that of the surfaces of all other Planets, taken together ? 
What Planet's surface comes next in magnitude to Jupiter's ? What Planet's sur- 
face is larger than that of our Earth, Venus and Mercury taken together ? What 
three Planets' surfaces taken together are smaller than that of the Moon ? What 
Planet has nearly as large a surface as the Moon ? 

[^ 13.] What is the opinion of philosophers respecting the Four Planets, Ceres, 
Vesta, Juno and Pallas ? 



LESSON III. 

EXPLAINING THE MOTION OF THE PLANETS AND COMETS ROUND THE SUN. 

^ 14. You have learned, in the preceding lesson, that the Earth and the 
other Planets are regularly moving round the Sun ; but you must know that the 
time which each requires to complete a whole revolution, that is, the time which 
each needs to move once round, cannot be the same with all ; as you may easily 
judge yourself: for the Planets which are next to the Sun will, of course, 
have a much smaller journey to perform, than those which are further from it. 
Thus Mercury, which is the first Planet in order from the Sun, will naturally 
come round much sooner than Jupiter, which is placed at a much greater distance 
from it. 

That you may the easier understand this, the following Plate, No. VI, will re- 
present to you our Solar System : 

The Sun from which proceeds all light and heat, is placed in the centre. 
Then come the Planets Mercury and Venus ; Third in order is our Earth 
with its Satellite the Moon ; and so on. The rest of the Planets in the 
same order in which they are represented on Plate II. You will also per- 
ceive there the orbs of two Comets, distinguished as you were told, by a tail of 



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Less. III.] IN ASTRONOMY. 9 

light. The Planets Jupiter, Saturn and Herschel are each represented with their 
Moons, and the Planet Saturn with its luminous ring. 

Now you will easily understand that Ceres, Vesta, Juno, Pallas, Mars, 
Jupiter, Saturn and Herschel, have each a much greater distance to travel, than 
our Earth ; but that, on the contrary, Venus and Mercury can complete their 
revolution in a much shorter time.* 

§ 15. The time which our Earth needs to travel once completely round the 
Sun, (to finish one revolution) is called a Year. Such a year has three hundred 
and Sixtyfive days ; — and each of these days has again Twentyfour hours. 

You see from this that the revolution of the Earth round the Sun gives us a 
means of measuring time, by which we are able to bring order and regularity into 
our business and transactions of life. For the making of clocks and watches is 
but a late invention, and we should be left entirely in the dark as regards the 
history of former ages, and a great many people would, at this present moment, 
be incapable of forming a correct estimate of time, if Providence had not given 
to all this appropriate means of measuring it. 

§j 16. While the Earth needs a whole year for one revolution round the Sun ; 
Mercury requires but Eightyone days, and Venus only about two thirds of 
One of our years. Mars, on the contrary, needs for one of his revolutions al- 
most Two years ; Vesta almost Four ; Juno, Ceres and Pallas over Four years ; 
Jupiter almost Twelve, Saturn over Twentynine, and Herschel nearly Eighty- 
four of our years ! f — And if these Planets, as we have reason to believe, are 
inhabited by beings endowed with human understanding and faculties, num- 
bering their years as we do ours — by the revolution of their Planets round the 
Sun — how different from ours must be the Period of their existence ! ! 



* If the teacher has an orrery at hand, if it be even of the most simple construction, he may exhibit it 
now. But it is the author's belief that a considerable portion of the pupil's interest is lost, if he be 
acquainted with it, at the beginning of the study ; or, as it is the custom in some schools, if an orrery is 
hung up among the charts and maps of the school room. The pupil ought not to see the orrery, until he 
knows that it is but a. faint illustration of the infinite grandeur of the heavens. Nothing detracts so much 
from our estimation of things as a too familiar acquaintance with them, before we know their real value. 

t The exact numbers are given in Table II, at the end of the book. 
3 



10 POPULAR LESSONS [Less. III. 

§ 17. During the time that the Earth is performing her journey round the Sun, 
the Moon, our constant attendant, is continually moving round the Earth, and 
completes one of these revolutions in little more than Tiventyseven days. — Very 
important and interesting to us are the changes in appearance which she exhibits 
during each of these revolutions. — You probably will know, that the Moon does 
not appear to us, at all times, the same. Sometimes she is hardly at all visible, 
(at least not with the naked eye) ; at other times only a small rim of her is 
seen, which by degrees becomes larger and larger, until finally she appears in 
her full round form. After this she begins again to diminish, changes again 
into a small luminous rim, and finally disappears entirely from our sight. These 
successive changes in the Moon's appearance are called the Moon's Phases, or 
the waxing and loaning of the Moon. The time during which the Moon is not 
seen is called New Moon ; the time during which she exhibits her full shape is 
called the Full Moon ; and the different periods of her waxing and waning 
(when she appears to us in the form of a crescent) are called Quarters. Thus we 
speak of the First and of the Last Quarter of the Moon. The First Quarter 
takes place after New Moon ; the last Quarter after Full Moon. 

The following diagram, Plate No. VII, may serve to represent to you the Moon's phases as 
seen from our Earth. 

When the Moon is in a, then the light of the Sun falls just on that side of it which is turned 
from the Earth. It is then, we have New Moon. When in b, a small brim of the Moon is seen, 
because a small portion of its lighted surface is then turned towards the Earth. — When in c half 
of her lighted surface is turned towards us, and we have the First Quarter. In d a still greater 
portion of the Moon's lighted surface is visible, and in e, we have Full Moon, because her 
whole lighted surface is then turned towards the Earth. In / the moon commences to wane 
(to grow smaller,) and in g the last quarter commences ; finally, when passed through the point 
h, we have in «, again New Moon. For familiar illustration you may also take a white ivory 
ball, holding it before a lighted candle, which may take the place of the Sun. When the 
ball is in a straight line between your eye and the candle it will appear to you all dark ; 
because the lighted part is then entirely turned toward the candle (away from you), and 
you have the same case which is represented to you in the diagram, when the Moon is in a. 
But if you move the ball a little to the right, you will perceive a streak of light, similar to the 
First Quarter represented in the Diagram, when the Moon is in c. If moved still farther to the 



Less. III.] IN ASTRONOMY. 11 

right, so that the whole lighted part of the ball is seen, it will resemble the Full Moon ; re- 
presented in the Diagram, when the Moon is in e. 

^18. While the Moon is moving round the Earth, it often occurs that she is 
placed in a direct line between ourselves and the Sun. In this case a greater or 
less part of the Sun is concealed from us, which causes a diminution of light or 
a partial darkness on our Earth. This we call an Eclipse of the Sun. (Such 
an Eclipse took place in 1831, and you will probably have an opportunity of 
seeing many more). If, on the contrary, the Earth is placed in a direct line 
between the Sun and the Moon, then the Moon will be obscured by our Earth. 
This is called an Eclipse of the Moon. The following two figures on Plate 
No. VIII will serve for an illustration. 

You will easily perceive from them that if the Moon (as represented in Figure I) is placed in 
a direct line between the Sun and ourselves, it must necessarily conceal from us part of that 
luminary ; and in this state cast a shade upon our Earth. 

But if the Earth is placed in a direct line between the Sun and the Moon, (as represented in 
Figure II), then the Moon will be much more obscured, because the Earth is much larger than 
the Moon, and will therefore cast a much greater shade upon her. 

^19. It remains for us to speak of that class of bodies known by the name 
of Comets, (see Lesson I, §6). Of these an unknown number belongs to our 
Solar System. — (Some philosophers have estimated their number to be about 
Twentyone ; others think it must amount to several hundred). They move 
round the Sun in exceedingly long ovals, having their transparent tails always 
turned away from that luminary. What is most remarkable about them is the 
astonishing degree of heat to which they are exposed on account of passing so 
near the Sun, and the astonishing velocity with which they travel. 

The Comet which appeared in the year 1680, is supposed to sustain a heat nearly Two 
Thousand times greater than that of red hot iron, and to move at the rate of several Hundred 
Thousand miles an hour ! ! 



12 POPULAR LESSONS [Less. III. 



RECAPITULATION OF LESSON III. 

QUESTIONS. 

[§ 14.] Do all Planets need the same time to complete a whole revolution 
round the Sun ? Why not ? 

If the pupils are old enough to understand the use of Dividers, it will perhaps be well for the 
teacher to let them draw the Solar System on a piece of paper. — If not, he ought to let them 
explain Plate IV, or an orrery, if one be at hand. 

[^ 15.] What is the time called, which our Earth needs for a complete re- 
volution round the Sun ? How many days are there in a year ? 'How many 
hours are there in a day ? 

What is the revolution of the Earth round the Sun, the means of ? 

[^ 16.] What time does Mercury require for a complete revolution round the 
Sun ? What time does Venus require for the same purpose ? What time does 
Ceres, Vesto, Juno and Pallas need ? What, Jupiter, Saturn, and Herschel ? 

[^ 17.] What motion does the Moon make whilst the Earth is travelling round 
the Sun ? How many days does the Moon need for a complete revolution round 
the Earth ? Does the Moon during its revolution round the Earth always exhibit 
the same shape ? What changes then does she gradually undergo ? What do you 
call the successive changes in the Moon's appearance ? What do you call the 
time during which the Moon is not seen ? What, that, during which she exhibits 
her full shape ? What, the different periods of her waxing and waning ? When 
does the First Quarter take place ? When the last ? 

[The teacher might now require the explanation of Plate V ; the elder pupils may draw the 
Diagram.] 

[^ 18.] What does frequently occur during the Moon's motion round the Earth ? 
What is the consequence of the Moon's position in a direct line between the Sun 
and ourselves ? What is such a diminution of light in consequence of the Moon 
being placed between us and the Sun, called ? What takes place when the 



Less. IV.] IN ASTRONOMY. 13 

Earth is placed between the Sun and the Moon ? What is such an obscuration 
of the Moon, in consequence of the Earth's position between her and the Sun, 
called ? 

[The younger pupils ought now to explain Plate VIII ; the elder pupils ought to draw the 
Diagram on a slate or paper.] 

[^ 19.] Is the number of Comets belonging to our Solar System precisely 
ascertained ? How many are there supposed to belong to our System ? In 
what manner do they move round the Sun? What remarkable property do they 
possess ? 



LESSON IV. 



ROTATION OF THE SUN, THE EARTH, AND THE REST OF THE PLANETS ON THEIR AXES. — DAY 
AND NIGHT. — INCLINATION OF THE EARTH'S AXIS. — SEASONS. 

^ 20. Besides the progressive motion of the Planets, of which we have spoken 
in the last Lesson, they have yet a peculiar motion like a wheel turning on its 
Axle-tree. This motion is called the rotation of the Planets on their Axes ; be- 
cause each of them seems to move round a straight line passing through its 
centre ; like a ball turning round a piece of wire run through the middle of it. — 
Moreover it is customary to call such a straight line imagined to be drawn 
through the centre of a Planet — the Axis of that Planet. 

The double motion of the Planets. — progressive and rotary, — is perhaps one of the most 
difficult things for young pupils properly to understand, without some popular illustration. If the 
teacher, therefore, has no orrery to show this motion to his pupils, he may compare it to a screw 
which is turned round whilst it suffers at the same time a progressive motion ; or perhaps with 
more propriety to a spinning-top, which is continually turning on its Axis, while at the same 
time it describes large circles.* 

* The propriety of this comparison becomes still more evident, when we reflect that the Axis of the 
top is generally somewhat inclined to the plane. 
4 



14 POPULAR LESSONS [Less. IV. 

^21. If you have well understood what has just been said, you will be 
able to comprehend, that our Earth, while it is performing its great journey 
round the Sun in Three Hundred and Sixtyjive days, is, at the same time, 
every Twentyfour hours turning on its Axis. This rotary motion of our Earth 
on its Axis is the cause of the successive changes of day and night ; that portion 
of the Earth which is turned toward the Sun having always day, when the other, 
which is turned away from him, has night. 

This is again a wise dispensation of God's providence. For if the Earth would always keep 
the same relative position to the Sun, then that portion of it. which would then be turned toward 
the Sun, would have continual day, whilst the other, which would then be turned away from 
him, would be enveloped in perpetual darkness. But as it is now arranged by the Earth's ro- 
tation on its Axis, most every portion of its surface must at least once every Twentyfour hours 
be turned toward the Sun and receive from him light and heat. Without this, one great half of 
our Earth would have a perpetual winter, destructive to plants and animals, while an everlasting 
summer would scorch the other half and render it equally unfit for the support of man. 

The following Diagram, Plate IX, may serve to give you an idea of the Earth's 
rotation round its Axis, and the alternate succession of Day and Night, resulting 
from it. When the Earth is situated as represented in the Diagram, then that por- 
tion of it, which is marked A, will have Day, because it is turned toward the Sun ; 
and the portion marked B, will have Night. But in the course of the next Twelve 
hours the order will be reversed. The portion which is marked B, will be 
turned toward the Sun and have day, whilst the portion A will be turned from 
him, and have night. 

^ 22. The rotation of the Earth on its Axis is also the cause of the Rising 
and Setting of the Sun. For no portion of our Earth is at once turned toward or 
from the Sun ; but moves toward or from it by degrees (as you may see by slowly 
turning a ball near the flame of a candle). This gradual motion of each portion 
of the Earth's surface toward or from the Sun, makes the Sun himself ap- 
pear to us as rising and going down ; while, in fact, we ourselves are turn- 
ing towards, or receding from him. This is a kind of deception similar to 
that which you experience when slowly gliding down a river ; when the objects 
on shore have the appearance of receding from you, while in fact, it is you, 
yourself, who are travelling away from them. 



Less. IV.] IN ASTRONOMY. 15 

The gradual rise and setting of the Sun is another excellent provision of nature. Were we 
from the darkness of night at once exposed to the luminous rays of the Sun, it would dazzle our 
eyes and render them unfit to distinguish a single object. — It is only by a gradual transition 
from darkness to light that we are able to accustom our eyes to the brilliancy of noon. 

^ 23. There is another peculiarity in the situation of our Earth with regard to 
the Sun, which you have not yet learned. The Earth's Axis is not even 
(parallel) with that of the Sun ; but is somewhat inclined towards it, as re- 
presented in the last Diagram. To this is owing the Change of the Seasons. 
For on account of the inclination of the Earth's Axis, the Sun's rays fall, some- 
times nearly perpendicular upon us, while at other times they are striking us 
more obliquely *. This is the principal cause of those changes of temperature 
which we are in the habit of distinguishing by the names, Spring, Summer, Au- 
tumn and Winter. 

In winter the Sun's rays strike us most obliquely ; it is therefore the coldest season of the 
year. In summer they are most perpendicular; — Summer therefore is the hottest season. 
Spring and autumn are standing in the middle between these two. From spring till mid-summer 
the Sun's rays are striking us more and more perpendicularly ; from mid-summer till winter more 
and more obliquely. 

A similar change of temperature is felt every day from Sun-rise (when the Sun- 
beams are most oblique) till noon, (when they are most perpendicular) ; and from 
noon again towards evening or Sun-set, when they are again oblique. 

^ 24. It has been mentioned (Lesson IV, ^ 20), that each Planet in our Solar 
System is regularly turning on its Axis. But all of them do not perform this 
rotation with equal velocity. The Planets which are farther from the Sun are 
turning quicker than those which are near him. Jupiter, for instance, turns on 
its Axis twice as fast as our Earth. The nights in Jupiter, therefore, do not last 
half as long as ours. 

This is, in some degree, necessary. For in proportion as a planet is further from the Sun, it 



* If the terms perpendicular and oblique, should not be perfectly understood by the pupils, it will be easy 
for the teacher to explain their meaning. 



16 POPULAR LESSONS [Less. IV. 

receives less light and heat, which deficiency is, in part, made up by a more frequent exposition 
to his rays. 

§ 25. The Sun himself is also known to turn regularly on his Axis, and to 
complete one whole rotation in about Twentysix of our days. This we have 
been able to perceive from the spots which have been discovered on its surface, 
and which gradually move toward and disappear on one side, when in a short 
time after they appear again on the other. 

^ 26. The Moon, and the Satellites of the other Planets have no rotary 
motion ; but have always the same side turned towards their Planets. Thus the 
moon keeps constantly the same side turned towards the Earth ; but her monthly 
motion round the Earth (Lesson III, ^ 17) is equal to a rotation on her axis ; be- 
cause by this means every part of her is, at least, once every Twentyseven days 
turned toward the Sun ; as you may see from the Moon's phases, represented on 
plate VII. A day in the Moon, therefore, is equal to Twentyseven of our days ; 
because the Moon moves in Twentyseven of our days round the Earth, which 
is equal to turning once on her axis. 



RECAPITULATION OF LESSON IV. 

QUESTIONS- 

[^ 20.] Is the progressive motion of the Planets round the Sun the only one 
which they are performing ? What other motion have they besides this ? What is 
this motion called ? Why is it called so ? What do you call a straight line 
imagined to be drawn through the centre of a Planet ? 

To what may the double motion of the Planets' progression and rotary be compared ? 

[^ 21.] What time does the Earth need to turn once on its axis ? How many 
times does the Earth turn on its axis during its whole journey round the Sun ?* 



* If the Earth requires 365 days to travel round the Sun ; and each day has twentyfour hours ; then the 
Earth will, during the whole of this time, turn Three Hundred and Sixtyfive times on its axis. 



Less. IV.] IN ASTRONOMY. 17 

What is this rotary motion of our Earth the cause of ? Which portion of the 
Earth has day ? Which night ? 

What would be the case, if the Earth was always to keep the same relative position with re- 
gard to the Sun ? What is the advantage derived from the rotation of the Earth on its Axis. 
Would the Earth be habitable without it or not ? 

[The pupil ought now to explain plate IX.] 

[§ 22.] What is the rotation of the Earth on its axis further the cause of? 
What does the gradual motion of each portion of our Earth towards the Sun 
produce ? 

What would be the case, if from the darkness of night we were at once exposed to the 
luminous rays of the Sun ? Could our eyes endure the brightness of noon without a gradual 
transition from darkness to light ? 

[^ 23.] What other peculiarity is there in the situation of the Earth with re- 
gard to the Sun ? What is this the cause of ? Do the rays of the Sun strike 
us at all times equally perpendicular or obliquely ? What changes of temperature 
are thereby created ? 

How do the rays of the Sun strike us in winter ? What season, therefore, is it ? How do 
the rays of the Sun strike us in summer ? What season, therefore, is summer with regard to 
temperature ? How are the rays of the Sun striking us from spring till mid-summer ? How, 
from mid-summer till winter ? What similar change of temperature do we experience every day 
from Sun-rise till noon, and from noon till evening or Sun-set ? 

[^ 24.] Do all Planets turn on their axes with equal velocities? Which Planets 
turn quicker, those which are nearer or those which are further from the Sun ? 
Give an instance. How long are Jupiter's nights in comparison to our's ? 

Why is this, in some degree, necessary ? 

[^ 25.] Is the Sun himself also known to turn on its axis like the Planets ? 
How many days does he need for one complete rotation ? By what means have 
we been able to observe this motion ? 

[^ 26.] Have the Moon and the Satellites of the other Planets also a rotary 
motion ? In what position does the Moon remain with regard to the Earth ? 
But what is her monthly revolution round the Earth equal to ? Why ? What is 
a day in the Moon equal to ? Why ? 
5 



18 POPULAR LESSONS [Less. V. 



LESSON V. 

OF THE APPEARANCE AND PECULIARITIES OF THE MOON AND SOME OF THE PLANETS WHEN 
VIEWED THROUGH A TELESCOPE. 

§ 27. Next to the Sun there is no heavenly body so interesting to us as the 
Moon. When viewed through a good Telescope * she has nearly the same 
appearance as in Figure I, Plate X. The bright parts are supposed to be 
lofty mountains and tracts of land ; (which is evident also from the shadow 
which they cast) and the dark spots are supposed to be valleys and caverns. 
Many of the mountains of the Moon are higher than the largest mountains 
on the Earth. Some of them are volcanos, and their eruptions have been dis- 
tinctly observed by many distinguished Philosophers. Some of the caverns are 
ascertained to have a depth of many miles and a width of almost Three miles. — 
No water has as yet been discovered in the Moon. Hence if she is inhabited, 
as we have reason to believe, her inhabitants must be very differently constructed 
from ourselves. 

^ 28. Among the Planets Venus is by far the most beautiful in appearance. 
She is known also by the name of the Morning and Evening Star. Her light is 
so bright that she is often seen at Noon. When viewed through a good telescope 
she exhibits phases similar to those of the Moon (Lesson III, ^ 17), which 
proves her spherical form (Lesson I, ^ 3). The mountains in Venus have been 
calculated to be at least Six times as high as those on our Earth. Her Atmo- 
sphere is only half as dense as ours. 

^ 29. Mars appears in many respects similar to our Earth. His light is red 
and changeable ; his surface exhibits black changeable spots (see Figure IT, 
Plate X). Some philosophers pretend to have noticed a region of ice on his 
poles. His atmosphere is twice as dense as ours. 

^ 30. Jupiter, viewed through a telescope, exhibits a surface covered with 
stripes. These are supposed to be clouds. A representation ol them is given in 



* This is an instrument through which we can see things much clearer and larger than we could with the 
naked eye. 



Less. V.] IN ASTRONOMY. 19 

Fig. Ill, Plate X. His light is very white and subject to but little variation. His 
atmosphere is nearly Twentyseven times denser (thicker) than ours. 

^51. Very remarkable, as we have already observed, is the Planet Saturn, 
on account of its luminous ring. Viewed through a telescope it has the appear- 
ance, represented in Figure IV. It is highly probable that to the inhabitants of 
that Planet, this ring has an entirely different appearance from what it has to us. 
It appears to be a solid opaque mass, and is probably inhabited like the Planet, 
which it constantly accompanies on its journey round the Sun. Saturn's atmo- 
sphere is nearly Ninety times denser than that of our Earth. No mountains have 
as yet been discovered on its surface. 



Herschel is too remote, for us to know much about its surface. Its atmosphere is supposed 
to be Three Hundred and Sixty-one times thicker than ours. 

Mercury, being the nearest Planet to the Sun, has a very bright light ; but is only seen early 
before Sun-rise, and immediately after Sun-set. It exhibits Phases like the Moon. 



RECAPITULATION OF LESSON V. 

QUESTIONS. 

[^ 27.] What do you know about the Moon's surface ? What, about its 
mountains, volcanos and caverns ? Have any great waters been discovered in it ? 

[^ 28.] What do you know about the Planet Venus ? By what other name is 
she known ? What does she exhibit, when viewed through a telescope ? What 
do you know about her mountains ? What, about her atmosphere ? 

[^ 29.] What do you know about the Planet Mars ? What, about his light, 
surface and atmosphere ? 

[^ 30.] What surface does Jupiter exhibit when viewed through a telescope ? 
Of what color is the light of Jupiter ? What do you know about his atmosphere ? 

[^ 31.] What do you know about the Planet Saturn ? What does the ring of 
Saturn appear to be ? What do you know about the atmosphere of this Planet ? 



20 POPULAR LESSONS [Less. VI 



LESSON VI. 

DESCRIPTION OF THE EARTHS SURFACE. — DIVISION OF IT INTO ZONES — TORRID, TEMPERATE 

AND ARCTIC ZONES. — THE FIVE GREAT CONTINENTS. — RELATIVE DIMENSIONS OF 

AMERICA, EUROPE, ASIA, AFRICA AND AUSTRALIA. 

^ 32. Having learned the relation of our Earth to the Sun and the Planets, 
it will be well to acquaint ourselves with the principal objects on its surfaces. — 
What the Interior of our Earth consists of, we have as yet no idea, because 
we have not yet been able to penetrate deeper than a few hundred feet ; and this 
is, in proportion to the Earth's Diameter, little more than nothing. But as 
regards her surface, we know that it consists partly of land and partly of water. 
Little more than one fourth of the Earth's surface is covered with land ; all the 
rest is water. — The great lands are called Continents ; the great waters are 
called Oceans. Smaller portions of land surrounded on all sides by water, are 
called Islands. Smaller bodies of water surrounded by land are called Lakes. 

% 33. The land on our Earth is divided into Five Continents : America, Eu- 
rope, Asia, Africa and Australia. — These, however, are not all of the same 
extent. Europe is the smallest of them. America and Asia are the greatest. 

The adjoining Plate No. XI, will give you an idea of the proportion of land and water on our 
Earth, and of the relative extent of the Five Continents. 

Fig. I represents the surface of the Earth divided into land and water. Were all land on our 
Earth put together in a circle, and the water placed round it, then the land would only fill the 
inner circle, the water occupying the surrounding ring, a space nearly four times as large as 
the circle. Fig. II, III, IV, V and VI represent the comparative surfaces of America, Europe, 
Asia, Africa and Australia. Fig. VII represents the comparative surface of the Moon. 

Upon close inspection of these figures you will perceive ; 

1. That the extent of America and Asia are nearly equal ; but that each of 
these Continents is several times larger than either Europe or Australia. 

2. That the next greatest portion of our Globe is Africa, which is more than 
three times larger than Europe. 

3. That Europe is the smallest Continent of our globe. 

4. That the whole surface of the Moon would not be more than enough lo 
cover either America or Asia. 



l''u/. /. 








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Less. VI.] IN ASTRONOMY. 21 

^ 34. The Earth's surface is not throughout equally illumined or heated by the 
Sun ; because the Sun's rays strike some portions of the Earth more perpendicular 
than others. Our Earth, therefore, is divided into Climates or Zones, which 
you will understand better from Plate XII. 

You will see from it that the Sun's rays are perpendicular to the central part of 
the Earth's surface ; but that toward the extremities of the Earth's Diameter 
these rays strike us more and more obliquely. The greatest heat, therefore, 
must be felt by the people living between the two circles EF and IK. The circle 
GH, which is exposed to the perpendicular rays, is termed the Equator ; and the 
two circles EF and IK, ivhich are at equal distance from the Equator, are called 
Tropic Circles. The whole surface included by these two circles is called the 
torrid Zone. The space between either of the circles CD and EF, or IK and 
LM, is called a temperate Zone ; because the Sun's rays striking these portions 
neither perpendicular nor very obliquely, their inhabitants suffer neither great 
heat nor cold. In one of these Zones are situated the United States of America 
and the greater portion of Europe. Beyond them, toward the extremities of the 
Diameter AB, are the two icy or arctic zones. The Sun's rays strike them 
very obliquely ; which is the cause of their being almost continually covered with 
ice or snow. 

The two circles, CD and LM, are called Polar circles ; and the two extremities, 
A and B, of the Earth's Diameter, situated in those regions, are called the 
Poles. A is called the North-Pole and B the South-Pole of the Earth. 

^ 35. The different zones of which we have just spoken, are not equal to one 
another. Plate XIII, will show their relative extent. 

Fig. I represents the surface of the Earth divided proportionally into its three zones : the 
torrid, the temperate and the arctic. The inner circle represents both the arctic zones ; the 
yellow ring b, which surrounds it, represents the united extent of the two temperate zones ; and 
the outmost red ring, the whole of the two torrid zones. 

Fig. II represents separately the whole torrid zone ; — Fig. HI one of the temperate zones ; — 
Fig. IV one of the arctic zones ; and Fig. V the whole extent of land on our globe. 

The next Plate, No. XIV, represents the comparative surfaces of these zones, drawn separately 
in form of squares ; and the last figure on that Plate, shows the extent of the five continents, 
compared to one of the temperate zones. 
6 



22 POPULAR LESSONS [Less. VI. 

You will observe from a close inspection of these figures, that the whole extent 
of land on our globe is nearly equal to that of a temperate zone ; and that if it 
were possible to unite America, Europe, Asia, Africa and Australia into one, their 
united extent would not jet fill one of the temperate zones ! You will also perceive 
that the two temperate zones occupy together the greatest portion of the Earth's 
surface, and that the arctic zones occupy comparatively the smallest. 

RECAPITULATION OF LESSON VI. 
QUESTIONS. 

[^ 32.] Do we know anything about the Interior of our Earth ? Why not f 
What does the surface of our Earth consist of ? What proportion does the land 
bear to the water? What are the great lands called? W 7 hat, the great waters? 
What are smaller portions of land, surrounded by water, called ? What, small 
portions of water, surrounded by land ? 

[^ 33.] Into how many continents is all the land of our Globe divided ? What 
are they ? Are all the continents of our globe of the same extent ? Which is 
the smallest of them ? Which are the largest ? Explain Plate, No. XI. 

What proportion does the extent of America bear to that of Asia ? What 
relation do these continents bear to Europe or Australia ? W T hat is the next 
greatest portion on our globe ? Which continent is the smallest ? What relation 
does the surface of the Moon bear to America or Asia ? 

[^ 34.] Is the whole Earth equally illumined or heated by the Sun ? Why not? 
What is, therefore, the surface of our Earth divided into ? Upon what portion 
of our Earth do the Sun's rays fall perpendicular ? What portion do they 
strike more obliquely ? What people, therefore, will experience the greatest heat ? 

[The pupil ought now to explain Plate XII. The elder pupils ought to draw a sphere with 
the Equator, the tropic and arctic circles. They ought also to draw the Diameter of the Earth, 
and indicate the North and South Pole.] 

[^ 35.] If you compare the whole extent of land on our globe to the Con- 
tents of one of the temperate zones, what proportion do }ou find them to bear to 
each other ? If it were possible to unite the five great continents, America, 
Europe, Asia, Africa and Australia, what zone would they nearly fill ? What two 
zones occupy the largest portion of the Earth's surface ? W T hat two, the smallest? 



Appendix.] IN ASTRONOMY. 23 



APPENDIX 

CONTAINING THE COMPARATIVE POPULATION OF THE DIFFERENT QUARTERS OF OUR GLOBE. 
[The numbers are given in Table III.] 

<§> 36. The Five principal parts of our globe, America, Europe, Asia, Africa and Australia 
are not equally thickly settled. Europe and Asia have, in proportion to their extent, the greatest 
population ; America and Australia the least. — The following Plate, No. XV, shows the com- 
parative population of these continents. 

Fig. I represents the whole surface of land on our globe, inhabited by nearly One Thousand 
Millions (One Billion) human beings. If these were to live throughout as close together as in 
Europe, then they would only occupy a surface of land as large in proportion, as the inner circle 
marked rt. But the two rings, b and c, occupy each as much surface as the circle a ; hence there 
is yet room for twice as many human beings ; before each quarter of the world is as thickly settled 
as Europe. 

Fig. II represents Asia and its population. If this quarter were settled as thickly as Europe 
is, then its inhabitants would only fill the inner circle marked b ; the ring a, therefore, is still left 
for settlement. 

Fig. Ill exhibits the population of Africa. If the inhabitants of this continent lived as close 
together as those of Europe, they would only fill the inner circle, marked c, and the surrounding 
ring might yet be inhabited. 

Fig. IV shows the comparative population of America. Its inhabitants, crowded together as 
the inhabitants of Europe, would only occupy the small circle e ; the whole broad ring /, there- 
fore, is still left for settlement ! ! 

Fig. V represents Australia. Its inhabitants, settled as in Europe, would only fill the circle a. 

Fig. VI represents the population of Europe filling the whole of that Quarter. 

The whole of these Six figures may represent to the pupil the comparative extents of the five 
great continents of our globe ; but the inner circles of these figures, and the whole of the sixth 
figure, show their comparative populations. From a close inspection of this plate the pupil 
may learn : 

1. That the population of Asia is yet greater than that of all the rest of the world. (The 
circle b in figure II being yet larger than the inner circles of all the other figures, and figure VI 
taken together.) 

2. That the population of Europe is as yet larger than that of America, Africa and Australia, 
taken together. 

3. That the population of Africa is larger than the joint populations of America and Australia. 

4. That America if once settled as Europe is, will have more than Six times her population. 

[The teacher, if he think proper to ask the pupils some questions in reference to the Appendix, will find 
no difficulty in adapting them to the capacity of his pupils.] 



TABLE I. 

Showing the Diameter, Surface, and Cubic Contents of the Sun and the 
Planets. 



Names. 


Diameter in Geographical 
Miles. 


Surface in Geographical 
Square Miles. 


Cubic Contents in Geographical 
Cubic Miles. 


Sun, 


194,000 


118,093,000,000 


3,825,903,253,970,000 


Mercury, 


608 


1,161,314 


117,659,099 


Venus, 


1678 


8,844,063 


2,473,469,743 


Earth, 


1719 


9,282,066 


. 2,659,159.061 


Mars, 


1006 


3,178,805 


532,996,317 


Vesta, 


74 


15,000 


2,121,347 


Juno, 


309 


282,690 


2,355,750 


Ceres, 


352 


389,182 


22,832,034 


Pallas, 


465 


650,266 


52,886,472 


Jupiter, 


19566 


1,202,280,406 


23,533,143,597,631 


Saturn, 


17263 


936,530,620 


2,757,547,946,775 


Herschel, 


7564 


173,696,911 


1,359,227,438,858 


Moon, 


480 


723,686 


51,561.578 



TABLE II. 

Showing the exact Duration of the Revolutions of the different Planets round the Sun. 



Planets. 


Years. 


Days. 


Hours. 


Min. 


Sec. 


Duration of the Moon's revolution 
round the Earth. 


Mercury, 


— 


87 
224 


23 

16 


15 

49 


44 

10 


27 days, 7 hours, 43 


Earth, 


1 




6 


9 


8 


minutes, and 12 


Mars, 


1 


321 


22 


18 


31 


seconds. 


Vesta, 


3 


225 


— 


— 


— 




Juno, 


4 


131 


10 


30 


— 




Ceres, 


4 


220 


13 


4 


— 




Pallas, 


4 


221 


15 


35 


— 




Jupiter, 


11 


314 


20 


39 


— 




Saturn, 


29 


166 


2 


— 


— 




Herschel, 


83 


266 


9 


— 


— 





TABLE III. 

Showing the Extent and Population of the five great Continents. 



Names of the Continents. 

America, 

Europe, 

Asia, 

Africa, 

Australia, 

The United States, 


Extent in Sq. Miles. 

14,868,000 
3,292,000 
15,000,000 
11,267,900 
3,823,200 

1,781,926 


Population. 

40,000,000 
198,000,000 
500,000,000 
150,000,000 
1,500,000 

13,000,000 



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operation from our common ciphering books or arithmetics, which is neces- 
sary for the practical purposes of life, and which is absolutely indispensa- 
ble to the merchant, the trader, and to the man of business in general. 

Exercises in Algebra, for Schools; with a Key, for the 
use of the teacher. By Francis J. Grund. 

The problems in algebra arc selected in particular reference to what is 
required for admission into American colleges. They are arranged in such 
ittle aid is required from the instructer ; the most dif- 
ained in the book. There is certainly no treatise on 
algebra, in t winch contains sufficient problems or 

exercises for the learner, the only means by which he may be expected to 
fit himself for the study of those branches which involve more difficulties — 
and perhaps the only way by which he can become accustomed to apply 
his knowledge of mathematics to practical purposes. 

An Elementary Treatise on Geometry. Simplified for 
Beginners not versed in Algebra. Part I. Containing Plane 
Geometry, with its Application to the Solution of Problems. 
By Francis J. Grund. Second Edition. 

An Elementary Treatise on Geometry. Simplified for 
Beginners not versed in Algebra. Part II. Containing Solid 
Geometry, with its Application to the Solution of Problems. 
By Francis J. Grund. 

(At a meeting of the School Committee of the city of Boston, Mr. 
Grund's Geometry was recommended as a suitable book to be used in the 
Public Schools. Similar testimonies to the" merits and usefulness of the 
work have been received from Teachers and School Committees in various 
parts of the Union.] 

Arithmetical and Algebraical Problems and Formula. 
Translated from the last German Edition of Meier Hirsch, 
and adapted to the Use of American Students. By F. J 
Grund, Author of ' A Treatise on Plane and Solid Geometry.' 
In 1 vol. 12mo. 



Mathematical Tables. Comprising Logarithms of Num- 
bers. Logarithmic Sines, Tangents, and Secants, Natural 
Sine's, Meridional Parts, Difference of Latitude and Depar- 
ture, Astronomical Refractions, &c. 

The Political Class Book, designed to instruct the higher 
classes in Schools in the origin, nature and use of Political 
Power. By William Sullivan, Counsellor at Law. 

The object of the Political Class Book is to point out to the young, who 
are in the course of education, their relation to each other, to society, and 
to their country ; and to show, in a plain and simple way, the excellence 
and value of the political condition in which they exist. The further pur- 
pose is to give some information of the social system of which they are to 
become active members, and on which their happiness absolutely depends. 

" The library of no citizen is complete where this work is wanting, and 
if the shelf contains no more than a Bible and an Almanac, the householder 
should not attend a town meeting until he has at least read the Political 
Class Book."— Mass. Spy. 

It has been proposed in the Legislature of Massachusetts to order, by law, 
its introduction into all the public schools of the State. 

The Moral Class Book, or The Law of Morals, derived 
from the created Universe and from Revealed Religion. In- 
tended for Schools as well as private reading. By William 
Sullivan, LL. D. Second Edition. 

In proof of the value of this work, and its adaption to the purposes ol 
general instruction, the Edinburgh Journal has commenced the republica- 
tion of it complete, in a series of articles under the title of Popular Morals. 
"We have found this small volume, " ssye the editor on perusal, "to con- 
tain a far more simple, lucid, and impressive view of the morals of man, 
than any that exists in this country ; and we therefore feel that, in trans- 
ferring it entire to our pag*s, we are doing a service to our native literature. 

The Historical Class Book, containing Sketches of His- 
tory from the beginning of the world to the end of the Roman 
Empire, A. D. 476. By William Sullivan, LL.D., author 
of the Political, and also the Moral, Class Book. 
publishers' advertisement. 

This work is principally intended for the use of Schools. The author 
does not pretend that it contains any thing new, except the attempt to ap- 
ply the experience of ancient nations to the people of the United States, 
and thus to make it practically useful. 

To understand what the right discharge of duty is, and in what the pub- 
lic happiness consists, we must know what the causes of welfare are, and 
what the exposure. The former may be learned by comparing our own 
country with others ; and the latter, by studying the actions "of men on 
other men. In these respects the history of every nation is instructive. 
Perhajis no era in the history of this country has existed, when the subject 
could have been more profitably studied than the present. 

This is the First Part of the Historical Class Book, bringing the subject 
down to the end of the Roman Empire. Should the work prove useful, it 
will be continued hereafter. 



rXT* School Committees, Teachers, and others interested in 
Education, are invited to call and examine the above. Copies fit/- 
nished gratis for examination. 



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